We have the following case:
• We have a number and let this number be equal to x
• If this number is increased by 1/4 of itself, the number will be 30
And we have to find the value of the number x.
To find it, we can proceed as follows:
1. We can translate the situation into algebraic language as follows:
[tex]x+\frac{1}{4}x=30[/tex]When we say "increased by" we are adding a quantity to the original one.
2. And now, we can solve the equation as follows:
[tex]\begin{gathered} x+\frac{1}{4}x=30 \\ \\ \frac{4}{4}x+\frac{1}{4}x=30 \\ \\ x(\frac{4+1}{4})=30 \\ \\ x(\frac{5}{4})=30\Rightarrow\frac{5}{4}x=30 \\ \end{gathered}[/tex]3. Finally, we can multiply both sides by 4/5 as follows:
[tex]\begin{gathered} \frac{4}{5}\frac{5}{4}x=\frac{4}{5}(30) \\ \\ x=4(\frac{30}{5})=4(6)=24 \\ \\ x=24 \end{gathered}[/tex]4. We can check this as follows:
[tex]\begin{gathered} 24+\frac{1}{4}(24)=30 \\ \\ 24+6=30 \\ \\ 30=30 \end{gathered}[/tex]Therefore, in summary, the number is 24 (x = 24).
